Beware of the cheapest moving company. Basically you are buying a service and the less you pay the less you will get.
Cheap movers will usually cut corners on things like packing and supplies. They will most likely be in a rush and understaffed.
You risk damage to your household items when dealing with a cheap moving company.
Take a look first at what services you need from your mover. Can you pack your own home? That saves quite a bit. How about a moving pod? Saves a lot over a full service mover.
Determine exactly what services you want and then have licensed movers offer price quotes on the same services. Compare those movers price and reputation and go from there.
Search for an affordable moving company and not the cheapest moving company and you will end up much happier with your move.